A Framework for Fluid Motion Estimation using a Constraint-Based Refinement Approach

• Autorzy: Doshi Hirak , Nori Uday Kiran

Identyfikatory

DOI

10.22630/MGV.2023.32.3.2

• Języki publikacji: EN

Abstrakty

EN

Physics-based optical flow models have been successful in capturing the deformities in fluid motion arising from digital imagery. However, a common theoretical framework analyzing several physics-based models is missing. In this regard, we formulate a general framework for fluid motion estimation using a constraint-based refinement approach. We demonstrate that for a particular choice of constraint, our results closely approximate the classical continuity equation-based method for fluid flow. This closeness is theoretically justified by augmented Lagrangian method in a novel way. The convergence of Uzawa iterates is shown using a modified bounded constraint algorithm. The mathematical well-posedness is studied in a Hilbert space setting. Further, we observe a surprising connection to the Cauchy-Riemann operator that diagonalizes the system leading to a diffusive phenomenon involving the divergence and the curl of the flow. Several numerical experiments are performed and the results are shown on different datasets. Additionally, we demonstrate that a flow-driven refinement process involving the curl of the flow outperforms the classical physics-based optical flow method without any additional assumptions on the image data.

Słowa kluczowe

EN

fluid motion estimation; evolutionary PDE; image processing; augmented Lagrangian; bounded constraint algorithm

• Wydawca: Institute of Information Technology of the Warsaw University of Life Sciences – SGGW
• Czasopismo: Machine Graphics and Vision
• Rocznik: 2023
• Tom: Vol. 32, No. 3/4
• Strony: 17--43
• Opis fizyczny: Bibliogr. 22 poz., il., rys., wykr.

Twórcy

autor

Doshi Hirak

• Department of Mathematics and Computer Science Sri Sathya Sai Institute of Higher Learning, Andhra Pradesh, India

• https://orcid.org/0000-0002-2735-0735

autor

Nori Uday Kiran

• Department of Mathematics and Computer Science Sri Sathya Sai Institute of Higher Learning, Andhra Pradesh, India

• https://orcid.org/0000-0001-9991-4846

Bibliografia

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